When a reinforced concrete flexural member is designed against shear loads according to the AIJ standard for reinforced concrete structures, bond performance between reinforcing bars and concrete should be verified. The bond splitting strength in the AIJ standard is based on pull-out test results of longitudinal deformed bars embedded in concrete. The bond strength is evaluated as shear stress on the surface of the bars. On pull-out test of deformed bars, bond strength of the deformed bar in second layer is apparently lower than that of the bar in first layer because of influence of bond stress in the first layer. In the AIJ standard, the bond strength in the second layer is simply reduced multiplying by 0.6. However, on bending-shear test results of R/C beams, when the deformed bar in second layer cut off, the bar performs higher strength. That is because bond stress distribution in the first and second layers is different from the case that all the double layered bars are arranged continuously through the span of beam. On the other hand, although more than three layers of longitudinal bars are arranged in foundation beams these days, the provision in the AIJ standard doesn't show methods for the bars more than three layers. It is necessary to consider the bond stress in all the tension bars totally in order to evaluate the side-splitting bond strength.

 In this paper, evaluation method of the side-splitting bond strength is reviewed in order to examine bond performance of the R/C beams with multi-layered longitudinal bars including cut off bars.
 The previous pull-out test results and bending-shear test results were reviewed in order to avoid side-splitting bond failure of the beams arranged more than three layers and including cut off bars. As a result of the revision, a new method for evaluating tensile force of all the longitudinal bars at the side-splitting bond failure is proposed. In this method, the direct shear failure of the concrete at the reinforcement layer is considered rather than the bond stress of each bar. The tensile force at the bond failure is expanded and simplified from the bond strength provided in the Design Guidelines for Earthquake Resistant Reinforced Concrete Buildings Based on Inelastic displacement Concept published by AIJ in 1999. However, the bond stress on the bar surface should be verified for local bond failure of the cut-off bar, corner-splitting failure, and V-notch splitting failure. If bond strength of cut-off bar in the second layer is estimated higher than the present provision, although it is the result observed in the loading test of the beam, a problem may occur. The problem can be avoided when the proposed method is adopted.
 In order to examine the new method, the tensile force at the bond failure was applied to shear strength formula provided in the 1999 AIJ Guidelines. It is rational to avoid the side-splitting bond failure by examine the shear capacity of the beams. The 1999 AIJ guidelines provide T_x, which is the bond strength, in the shear strength formula. In this paper, the proposed method was applied to T_x. The modified shear strength formula is verified by comparing with the previous test results. The test results of the R/C beam specimens of single, double and more than three layers arrangement, and the specimens including cut off bar, were selected. As the results of comparison, the modified method shows good agreements with the test results with almost the same accuracy as the method in the 1999 AIJ guidelines.

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 There have been many pull-out tests of single and double layered deformed bars to investigate bond strength in R/C members^{2), 4)-10)}. In these tests, the development lengths of the bars were identical as shown in Fig. 1 (a). These tests indicated that the bond strengths in the second layer weakened as the stresses in the first layer became large. On the other hand, some of longitudinal bars at the end sections of an R/C beam are cut off in the span if those are no longer needed against required loads. In the previous experimental studies of R/C beams^{11), 12)}, it was indicated that maximum bond stresses in cut-off bars in the second layer were larger than those in bars placed through the span, as shown in Fig. 2. In order to evaluate the bond capacities of multi-layered reinforcing bars, a new method was proposed¹³⁾. This method is for evaluating the capacity of all the tension bars, and can be applied to tension bars including cut-off bars. However, the method may underestimate a bond capacity of a singly reinforced beam with cut-off bars, and tentative assumption was adopted for the method because of limited experimental studies.

 In this study, pull-out tests of reinforcing bars of different development lengths, as shown in Fig. 1 (b), were carried out. The specimens were intended for the condition in the beam including cut-off bars. Test variables were the number of layers, the number of bars in the second layer, development length, l_d, of bars in the first layer, shear reinforcement ratio, and concrete strength. Three bars were placed in the first layer in all the 28 specimens, and each test variable was as follows: single or double layers; two or three bars in the second layer; short l_d of 500mm or long l_d of 688mm; shear reinforcement ratios of 0.2%, 0.4% and 0.6%; specified concrete strengths of 21, 24, 36, and 54 N/mm². In this investigation, bond capacities in the range of 500mm that was the same as short l_d, was focused on. As a result of the monotonic pull-out tests, the following conclusions can be drawn.
 (1) When single layered reinforcement is not sparse arrangement, regardless of a mixture of short and long l_d, the bond strength of the short l_d bar can be evaluated by the calculation for side splitting failure with safe margin.
 (2) Regarding the double layered specimens, the bond strength of the bars in second layer can be evaluated by Tsuihiji formula⁹⁾ by substituting bond force ratio for load ratio between first and second layers.
 (3) In the specimen with different development length bars, total bond force in the range of 500mm reaches its peak before or at the same time as the peak of the bond stress of short l_d bar. Because the total bond force balances on truss action in an R/C beam, it is reasonable in design to evaluate the total bond capacity in terms of checking resistance of the member. However, an additional examining must be needed for a local failure of a cut-off bar.
 (4) The total bond capacity of double layered bars was larger than that of single layered bars. Effects of increasing shear reinforcement in single and double layered specimens were almost the same. However, the total bond capacity of tension bars of different l_d was smaller than that of identical l_d. Especially, the specimens which the mid bar in first layer was shorter than bars around it, showed lower capacities than the specimens with identical l_d bars by about 80%.

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